Abstract
We study computational methods for computing the distance to singularity, the distance to the nearest high-index problem, and the distance to instability for linear differential-algebraic systems (DAEs) with dissipative Hamiltonian structure. While for general unstructured DAEs the characterization of these distances is very difficult and partially open, it has been shown in [C. Mehl, V. Mehrmann, and M. Wojtylak, Distance problems for dissipative Hamiltonian systems and related matrix polynomials, Linear Algebra Appl., 623 (2021), pp. 335â366] that for dissipative Hamiltonian systems and related matrix pencils there exist explicit characterizations. We will use these characterizations for the development of computational methods to approximate these distances via methods that follow the flow of a differential equation converging to the smallest perturbation that destroys the property of regularity, index one, or stability.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: ETNA - Electronic Transactions on Numerical Analysis
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
